That exact part doesn't seem to exist, but if ZRB188R61A226ME05 is close enough, it shows a mere 8.9uF at 3.3V, and that will get much worse at elevated temperature (because it's only X5R) and with aging (maybe -20 to -50% over lifetime??). Probably another penalty due to the small voltages we're talking (capacitors are typically measured at 0.5Vrms, deeper into the hysteresis curve, raising the average capacitance that's measured). At 0.05V it's maybe -20%.
Personally, I would choose 0805 or 1206 size, X7R, >=10V, for this application.
In general, to reduce ripple voltage for a given transient current, you need to reduce the supply network impedance. This means reducing R and L, and increasing C. Dominant R and L are from the regulator's equivalent output impedance. C is from the capacitors of course.
You may find it's better to use smaller (1-4.7uF) caps in that size (0603), and X7R, for better stability, and simply using more of them. You don't need piddly bypass caps at all, with the supply planes and a few caps of any sufficient value dotted around. Can use just 4.7's everywhere, and leave a few DNP besides.
Nor does the regulator need one highly localized. It won't notice a couple 5nH of trace inductance, its impedance isn't nearly low enough, nor its bandwidth high enough.
Also, the difference due to measurement method seems to imply there's either differences by region (could be, there's different ESL to each capacitor on that plane), or common mode error (perhaps the transient current drawn from the supply is causing an offset voltage in the supply ground?). If CM, that may actually be significant because that can cause emissions problems.
Tim